Question

Given: arc IV =140°, arc VK =30°, m∠ISV=135, Find: m∠VPL

Answer 1

Answer:

The measure of the ${\angle}VPL$ is $80^{\circ}$

Step-by-step explanation:

We know that  the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

Now, Let

x is the measure of arc IV

and y is the measure of arc PK, then

$m{\angle}ISV={\frac{1}{2}}(x+y)$

Substituting the given values, we get

$135^{\circ}={\frac{1}{2}(140^{\circ}+y)$

$270^{\circ}=140^{\circ}+y$

$y=130^{\circ}$

Thus, The measure of arc PK is $130^{\circ}$.

Also, we know that  the inscribed angle measures half that of the arc comprising , thus

Let

z is the measure of arc VK

and  y is  the measure of arc PK, then

$m{\angle}VPL={\frac{1}{2}(z+y)$

Substituting the values, we get

$m{\angle}VPL={\frac{1}{2}}(30+130)=80^{\circ}$

Hence, the measure of the ${\angle}VPL$ is $80^{\circ}$.